326 BELL SYSTEM TECHNICAL JOURNAL 



For the case of maximum output at P = Q = — 

 Hi = 20 log ^ + 14. 



Accuracy of Computations 



Before closing the subject, let us consider for a moment the accuracy 

 involved. Very careful measurement of the characteristics of samples of 

 some tubes, notably the 310A and 807 has shown that over a large range the 

 fit with a parabola is excellent. On the other hand the electron tube bulle- 

 tins give characteristics which are avowedly average. The drafting errors 

 must be large and the temptation to use a straight edge instead of a french 

 curve must be great. Probably no two observers will agree as to the extent 

 of the straight part of a conductance curve. Even in the case of the 310A 

 and 807 tubes mentioned above, manufacturing variations may affect the 

 transconductance curve from tube to tube. 



With this in mind we may conclude that the results obtained, that is, the 

 values of the current obtained by the methods evolved above, must be ap- 

 proximate in character. The value of the analysis given lies in its simplicity 

 rather than accuracy. Admitting that the situation is not satisfactory from 

 the standpoint of reproducibility of results we must face the fact that there 

 is no method nor the promise of a method for computing performance of a 

 tube that would come within slide rule accuracy. We may console our- 

 selves that in practice accuracy in estimating output levels and unwanted 

 products is not really required. An error of 3 db or in the case of unwanted 

 products an error of 6 db is of small consequence. This is about the varia- 

 tion to be expected to exist between two individual electron tubes and it 

 must be included as a tolerance in determining performance requirements. 



In connection with the third-order modulation the question arises whether 

 the transconductance characteristic is really parabolic and not a curve of 

 fourth or sixth degree and, if so, whether the equations derived above still 

 apply. 



While no accurate test can be applied conveniently we may compare a 

 parabola with a quartic passing through the same three points. The parab- 

 ola is characterized by a smooth curvature, while the quartic and the higher- 

 degree curves have a flat middle portion with the ends turned up sharply. 

 An inspection of the transconductance characteristics of tubes reveals that 

 they are of the smoother curv^ature type — that is, that a square term is the 

 chief contribution to the series representing the curve. 



Should this not be the case and should we possibly mistake a quartic for a 

 parabola, we still would obtain all of the phenomena caused by third-order 



